TE Waves in Rectangular Wave Guide

AI Thread Summary
The discussion centers on the boundary conditions for magnetic fields at the surface of a perfect conductor, specifically why the normal component of the magnetic field, B_n, must equal zero at the boundaries (x = 0 and x = a). It is established that B_n is continuous at the boundary, leading to the conclusion that B_n = 0 just outside the conductor. The conversation clarifies that while B_n is zero, the tangential components of the magnetic field can still exist, meaning Bx and By do not necessarily equal zero along the axes. The participants emphasize the importance of understanding the distinction between normal and tangential components of the magnetic field in this context. Overall, the thread highlights the principles governing magnetic fields in the presence of perfect conductors.
unscientific
Messages
1,728
Reaction score
13
Hi guys I'm having difficulty understanding why the boundary conditions lead to dX/dx = 0.

Why must Bx = 0 at x = 0 and x = a?


jt5vr5.png
 
Physics news on Phys.org
B_n is continuous at a boundary, and B=0 inside a perfect conductor (which is assumed for these equations).
Therefor B_n=0 just outside the conductor.
 
And that is arisen from the fact that there is no magnetic dipole, i.e., the magnetic field is divergenceless. You can derive the continuity of the normal component of the magnetic field on the boundary by imaging a small pillbox on the boundary. Maybe Griffiths already described in Chap 5.
 
buoyant said:
And that is arisen from the fact that there is no magnetic dipole,
I know you meant monopole.
 
Thanks Achuz for noticing my mistake
 
Meir Achuz said:
B_n is continuous at a boundary, and B=0 inside a perfect conductor (which is assumed for these equations).
Therefor B_n=0 just outside the conductor.

Sorry, I don't get what you mean. If B_n is perpendicular to surface and = 0, then won't Bx = 0 and By = 0 along y-axis and x-axis correspondingly
 
Last edited:
unscientific said:
Sorry, I don't get what you mean. If B_n is perpendicular to surface and = 0, then won't Bx = 0 and By = 0

Only the normal component is continuous.. so B is parallel to surface at the boundary.
 
scoobmx said:
Only the normal component is continuous.. so B is parallel to surface at the boundary.

Yes, so along x-axis, By = 0, and along y-axis, Bx = 0?
 
Yes...
 
Back
Top